Cell cycle-specific phase separation regulated by protein charge blockiness

Dynamic morphological changes of intracellular organelles are often regulated by protein phosphorylation or dephosphorylation1–6. Phosphorylation modulates stereospecific interactions among structured proteins, but how it controls molecular interactions among unstructured proteins and regulates their macroscopic behaviours remains unknown. Here we determined the cell cycle-specific behaviour of Ki-67, which localizes to the nucleoli during interphase and relocates to the chromosome periphery during mitosis. Mitotic hyperphosphorylation of disordered repeat domains of Ki-67 generates alternating charge blocks in these domains and increases their propensity for liquid–liquid phase separation (LLPS). A phosphomimetic sequence and the sequences with enhanced charge blockiness underwent strong LLPS in vitro and induced chromosome periphery formation in vivo. Conversely, mitotic hyperphosphorylation of NPM1 diminished a charge block and suppressed LLPS, resulting in nucleolar dissolution. Cell cycle-specific phase separation can be modulated via phosphorylation by enhancing or reducing the charge blockiness of disordered regions, rather than by attaching phosphate groups to specific sites.

intrinsically disordered regions (IDRs) of proteins regulates LLPS mechanistically remains elusive [16][17][18][19] . Recent studies using charged polymers and theoretical modelling demonstrated that a polyampholyte chain with segregated charged residues (charge blocks) exhibits stronger phase separation than the chain with the same number of charged residues randomly distributed [20][21][22][23] . Charge blocks also play important roles in phase separation in vivo [24][25][26] , and shuffling of the charged residues along a polypeptide results in the dispersion of liquid-like organelles in the cell 24,25 . As many IDRs of cellular proteins are hyperphosphorylated during mitosis, for example, Ki-67, RIF1, INCENP and NPM1 16 , the addition of multiple negatively charged groups may enhance or reduce such 'charge blockiness' of IDRs and affect the propensity for LLPS in the cell. However, direct evidence for this hypothesis is lacking.
Ki-67, a nucleolar phosphoprotein, plays a critical role in organizing the periphery of mitotic chromosomes, which are thought to have a liquid-like property. Ki-67 separates chromosomes from each other and prevents their coalescence during mitosis [27][28][29][30][31][32] . Human Ki-67 is composed of multiple domains, including an N-terminal PP1-binding domain, a central repeat domain (RD) composed of 16 repeats of an ~110-amino-acid unit, and a C-terminal chromatin-targeting domain (LR domain) for chromosome binding (Fig. 1a). Phosphoproteomic analyses demonstrated that Ki-67 is hyperphosphorylated by CDK1 and other mitotic kinases 33 . Our quantitative mass spectrometric analysis of mitotic phosphorylation identified more than 70 residues in the RD that are significantly phosphorylated upon entry into mitosis 16 . Comparison of the charge distributions between the mitotic (hyperphosphorylated) form and interphase (dephosphorylated) form revealed that mitotic phosphorylation converts the individual repeats into strong diblock ampholytes, in which a positive charge block is followed by a negative block (Fig. 1b). This tendency was identified in most of the repeats present in the RD (Extended Data Fig. 1a), suggesting that mitotic phosphorylation enhances the alternating charge blocks throughout the RD. In contrast, mitotic hyperphosphorylation of nucleophosmin (NPM1), an IDR-rich nucleolar protein that interacts with Ki-67 and plays a critical role in assembling nucleolar components in interphase cells 34 , diminishes the alternating charge blocks that otherwise exist in the non-phosphorylated form (Extended Data Fig. 1b). Therefore, mitotic hyperphosphorylation may introduce negative charges to enhance or reduce the alternating charge blocks in the IDRs and modulate the propensity for LLPS (Fig. 1c). In this Letter, we tested the hypothesis that changes in charge blockiness, rather than the attachment of phosphate groups Recombinant proteins of human Ki-67 RD formed liquid-like droplets in vitro in the presence of 100 mM NaCl and 15% polyethylene glycol. (Fig. 1d and Extended Data Fig. 2a,b). Droplet formation increased with the number of repeats ( Fig. 1d and Extended Data Fig. 2c). Tandem homogeneous repeats of repeat 12 ((R12) 1 , (R12) 2 and (R12) 4 ) showed a similar tendency ( Fig. 1e and Extended Data Fig. 2d). A clear inverse correlation between the number of repeats and the propensity of LLPS (quantified by the saturation concentration, C sat 10 ) was observed; C sat sharply decreased as the repeat number increased (Fig. 1f,g). The effect of phosphorylation on LLPS was examined. R12 contains nine mitotic phosphorylation sites (Fig. 1b), six of which harbour a consensus motif for CDK1 35 . In vitro phosphorylation of recombinant R12 by CDK1 increased droplet formation (Fig. 1h and Extended Data Fig. 2e).
Phosphomimetic mutations in nine mitotic phosphosites (Pm9) in R12 enhanced droplet formation (Fig. 2a,b and Extended Data Fig. 3a). Phosphomimetic mutations in another repeat (R7) also    2 and 20 μM (R12) 4 ) (e) are shown. Scale bar, 30 µm. f,g, The turbidity of the droplet solution was measured as the OD 600 and plotted against the protein concentration (f). One representative result is shown for each construct (out of three). C sat , which represents the protein concentration giving a half-maximal OD value, was obtained by curve fitting and plotted against the repeat number (g). Error bars reflect standard deviation of the mean (n = 3 independent measurements). h, Wild-type R12 was incubated with aTP or aDP in the absence or presence of purified CDK1-cyclin B and subjected to LLPS assay. Scale bar, 50 µm. Source numerical data are available in source data.

Letters
NAturE CELL BioLogy enhanced LLPS (Extended Data Fig. 3b,c). Notably, the phosphomimetic mutations did not induce the formation of any secondary structures (Extended Data Fig. 3d). To demonstrate that alternating charge blocks are important and necessary for LLPS, we constructed a series of R12 mutants in which the charge distribution was modified by replacing the amino acids that are not involved in mitotic phosphorylation (charge-block mimetic mutant, CBm; Fig. 2a) and subjected these mutants to the LLPS assay ( Fig. 2b and Extended Data Fig. 3a). Neutralization of the positive charge block at the amino-terminal region by substituting either the neutral amino acids with glutamic acid (E) residues (CBm-1) or K/R by Q (CBm-2) reduced the formation of liquid droplets (Fig. 2b). In contrast, replacement of neutral residues in the middle region with E residues, which mimics phosphorylated charge blocks (CBm-3), substantially promoted LLPS, as was observed in the phosphomimetic mutant (Pm9). A similar effect was observed when E residues were introduced in the carboxyl-terminal region (CBm-4) (Fig. 2b).
The relationship between charge blockiness and LLPS was investigated quantitatively. The extent of charge blockiness along the polypeptide was evaluated on the basis of either the blockiness of like charges (B LC ) or degree of segregation (D seg ) (Methods). Plotting C sat against B LC and D seg revealed a clear inverse correlation (Fig. 2c and Extended Data Fig. 4a). To characterize the relationship further, a series of mutants (CBm-5-16) carrying different net charges (between −4 and +5) and/or charge blockiness (Extended Data Fig. 4b) were constructed and subjected to LLPS assay. C sat more closely correlated with charge blockiness (B LC and D seg ) ( Fig. 2d and Extended Data Fig. 4c) than with the net charge (Extended Data Fig. 4d). Together, these results demonstrate that the existence of alternating charge blocks governs LLPS in vitro and indicate that neither the exact position of the charged residues nor a negative shift of the net charge is a critical determinant.
Next, we tested whether the Ki-67 RD could form a liquid phase on an artificial chromosome surface in vitro. Diethylaminoethyl (DEAE) beads were coated with double-stranded DNA and incubated with LR-fused R12 (LR is necessary for DNA binding). All these constructs bound to the DNA-coated beads; however, both the phosphomimetic mutant (Pm9) and the charge-block mimetic mutant (CBm-3) assembled on the beads stronger than the wild type (WT) (Fig. 3a,b). As the mutation affected neither the affinity

NAturE CELL BioLogy
for DNA (Extended Data Fig. 5a) nor the efficiency of fluorescent labelling (Extended Data Fig. 5b), the protein layer observed in the Pm9 and CBm-3 sequences indicated stronger interactions among the RDs. To confirm this, fluorescently labelled LR-free (Pm9) 1 was added to the DNA beads together with non-labelled (Pm9) 2 -LR. The labelled (Pm9) 1 was incorporated into the layer only in the presence of (Pm9) 2 -LR (Extended Data Fig. 5c). The incorporation of LR-free molecules was stronger in Pm9 and CBm-3 than in WT (Fig. 3c,d). The liquid-like property of the protein layer was further confirmed by fluorescence recovery after photobleaching (FRAP) analysis of the LR-free molecules in the layer ( Fig. 3e and Extended Data Fig. 2b). We investigated how phosphorylation of the Ki-67 RD and its LLPS-promoting activity were related to the formation of the c-e, assembly and behaviour of LR-free R12 on a bead. λDNa-bound DEaE beads were incubated with purified LR-fused R12 ((WT) 2 , (Pm9) 2 and (CBm-3) 2 ), together with aTTO610-labelled LR-free R12 ((WT) 1 , (Pm9) 1 and (CBm-3) 1 ). Fluorescence and differential interference contrast (DIC) images are shown (c). Signal intensity of the protein layer along the bead's contour was measured and normalized to the median value of (Pm9) 1 (d) (n = 8). Box plot shows the minimum and maximum value by whiskers, 25% and 75% percentile by box boundaries and outlier by dot above upper whisker. Numbers above graph indicate P values by one-tailed Mann-Whitney U test. Representative fluorescence images acquired during the FRaP analysis are shown (e). The region surrounded by a circle was bleached and the fluorescence intensity in the area was measured and plotted with a solid line of mean and a shade of standard deviation (right panels) (n = 4 for (Pm9) 1 and n = 5 for (CBm-3) 1 ). Scale bar, 15 µm. Source numerical data are available in source data.
chromosome periphery in vivo. Enhanced green fluorescent protein (EGFP)-Ki-67 (full length) expressed in HeLa cells localized in the interphase nucleoli and at the mitotic chromosome periphery (Fig. 4a). The liquid-like behaviour of Ki-67 at the chromosome periphery was confirmed by treating the cells with ammonium acetate 36 , as well as by FRAP analysis (Extended Data Fig. 6a-c). The homogeneous repeats of R12 were fused with LR (required for binding to chromosomes; Extended Data Fig. 6d) and expressed in HeLa cells (Fig. 4b). These homogeneous repeats localized at the mitotic chromosome periphery in a repeat-number-dependent manner (Extended Data Fig. 6e). Replacement of all nine mitotic phosphosites with non-phosphorylatable residues ((A9) 12 -LR; Fig. 4b), which nearly completely abolished mitotic phosphorylation (Extended Data Fig. 7a), severely diminished the peripheral localization compared with that of the WT constructs containing the same number of repeats ( Fig. 4c and Extended Data Figs. 6e and 7b). In contrast, the phosphomimetic mutant (Pm9) 12 -LR, as well as a charge-block mimetic mutant showing similar LLPS in the in vitro droplet assay ((CBm-3) 12 -LR) (Fig. 2b), localized at the chromosome periphery (Fig. 4c). These results indicate that the block-polyampholyte repeat is necessary and sufficient for localization at the mitotic chromosome periphery. The ability to form a functional chromosome periphery was examined using Ki-67 knockout (KO) cells. In these cells, mitotic chromosomes coalesced, forming a large single mass of chromatin (Fig. 4d). The depletion caused a slight mitotic delay in some cell lines 37 , although other cell lines showed proliferation similar to that of the WT counterpart 38 . The expression of full-length Ki-67 in KO cells nearly completely rescued the phenotype (Fig. 4d). Three-dimensional morphological analysis of the mitotic chromosomes indicated that chromosomes were more dispersed in the rescued cells than in non-rescued cells (Extended Data Fig. 7c). The recovery of the chromosome periphery was confirmed by the segregated localization of protein and DNA on mitotic chromosomes (Extended Data Fig. 7d,e). Notably, WT R12 ((WT) 12 -LR), but not the non-phosphorylatable form ((A9) 12 -LR), rescued the KO phenotype (Fig. 4d), although to a lower level than the full-length Ki-67 did (Extended Data Fig. 7c,d), probably because of its lower repeat number. Homogeneous repeat of R7 ((R7) 12 -LR) not only localized at the chromosome periphery of mitotic HeLa cells, but also rescued the phenotype of Ki-67-KO cells (Extended Data Fig. 7c,d,f,g), suggesting that the number of repeats rather than specific amino-acid sequence of R12 is important for the formation of the chromosome periphery. Notably, not only the phosphomimetic mutant ((Pm9) 12 -LR), but also the charge-block mimetic mutant ((CBm-3) 12 -LR) of R12 rescued the KO phenotype ( Fig. 4d and Extended Data Fig. 7c, d). The charge-block mimetic mutant carrying the same net charge as A7 but larger charge blockiness (CBm-7; net charge +5 and B LC 35) also rescued the KO phenotype (Extended Data Fig. 7e), indicating that charge blockiness, but not a negative shift of the net charge, is critical for the formation of the chromosome periphery. Together, these results demonstrate that the alternating charge blocks of the Ki-67 RD are necessary and sufficient for efficient LLPS in vitro and for forming the functional mitotic chromosome periphery in vivo.
Next, we investigated whether mitotic phosphorylation regulates the intracellular dynamics of other phosphoproteins by changing the charge blockiness. NPM1 localizes in the GC region of the nucleoli and is heavily phosphorylated upon entry into mitosis 16 . Eleven mitosis-specific phosphorylation sites were identified in a long stretch of the IDR (Extended Data Fig. 1b). Comparison of the charge distributions revealed that the dephosphorylated (interphase) form has a strong block-polyampholytic charge distribution, whereas the hyperphosphorylated (mitotic) form loses positive charge blocks (Extended Data Fig. 1b). Therefore, mitotic hyperphosphorylation may reduce the propensity of NPM1 for LLPS, an effect opposite to that observed for Ki-67 (Fig. 5a). Indeed, CDK1-treated NPM1-IDR and the phosphomimetic mutant of the 11 mitotic phosphosites reduced the formation of liquid droplets in vitro ( Fig. 5b and Extended Data Fig. 8a-c). Notably, a charge-block mimetic mutant of NPM1 showed reduced droplet formation ( Fig. 5b and Extended Data Fig. 8b,c), demonstrating that mitotic phosphorylation suppresses LLPS of NPM1 by reducing its charge blockiness. We found that the intracellular dynamics of NPM1 during mitosis were also modified by phosphomimetic and charge-block

Letters
NAturE CELL BioLogy mimetic mutations (Fig. 5c). NPM1 diffused from the nucleoli into the cytoplasm when the cell entered mitosis and localized mainly in the cytoplasm, with weak localization around the chromosome periphery. It re-appeared at the chromosome periphery in anaphase and eventually assembled into many small loci in telophase (arrowheads in Fig. 5c), finally fusing to form several nucleoli in early G1 phase. Phosphomimetic and charge-block mimetic mutants localized not only in the nucleoli, but also in the nucleoplasm and cytoplasm in interphase cells (Fig. 5c). Similar to the WT, the mutants diffused into the cytoplasm during prophase and metaphase but did not re-assemble at the chromosome periphery even in anaphase and telophase and remained in the cytoplasm throughout mitosis. Finally, they started to localize to the nucleoli in early G1 phase (asterisk in Fig. 5c). These results demonstrate a close correlation between the block-polyampholytic property of NPM1 and its intracellular dynamics during mitosis. As Ki-67 directly or indirectly interacts with NPM1 via its N-terminal conserved domain (Extended Data Fig. 8d), we investigated how the opposing effects of mitotic phosphorylation on these proteins are integrated to determine their behaviour during mitosis. The homogeneous repeat construct of Ki-67 ((R12) 12 -LR) localized exclusively in the nucleoplasm in interphase cells (interacting with the chromosome via LR), and addition of the N-terminal domain (1−639) (NT-(R12) 12 -LR) directed it to the perinucleolar region (an interface between the nucleoli and nucleoplasm) (Fig. 5d), suggesting that Ki-67 bridges NPM1 and the chromosome. Ki-67 constructs were localized at the chromosome periphery in prophase and metaphase regardless of the presence of the N-terminal domain (Fig. 5d). In this period, the interaction between Ki-67 and NPM1 was severely abrogated (Extended Data Fig. 8d). When the interaction between Ki-67 and NPM1 recovered in anaphase and telophase, NT-(R12) 12 -LR re-assembled with NPM1 and finally localized in the perinucleolar region, whereas (R12) 12 -LR did not associate with NPM1 and was redistributed from the periphery to the entire chromosome until the end of mitosis (Fig. 5d), demonstrating that the perinucleolar localization of Ki-67 requires interaction with NPM1. Overall, these results suggest a reciprocal regulatory mechanism of the nucleoli and chromosome periphery during the cell cycle.
We demonstrated that mitotic hyperphosphorylation of the RD of Ki-67 enhanced its charge blockiness and promoted its LLPS to form the periphery of mitotic chromosomes. Notably, a mutant mimicking the mitotically phosphorylated charge blocks not only displayed strong LLPS in vitro (Fig. 2b,c), but also rescued deficiencies observed in Ki-67-KO cells (Fig. 4d). Thus, the occurrence of alternating charge blocks, rather than the exact position of negative charges, plays an important role in chromosome periphery formation via LLPS. This 'fuzzy' regulatory mechanism, regulated by charge blockiness, clearly contrasts the conventional 'tight' mechanism via which site-specific addition of a phosphate group modulates stereospecific interactions between structured proteins or domains. This mechanism is distinct from a previously reported mechanism of multiple phosphorylation, in which stepwise accumulation of multiple phosphate groups confers high cooperativity or ultrasensitivity in enzymatic activation (such as that for the CDK1 inhibitor Sic1 (ref. 39 )). The proposed mechanism also explains why protein phosphorylation frequently occurs at multiple neighbouring residues located in IDRs [40][41][42] .
Notably, the mode of cell cycle-dependent regulation is reversed in NPM1: mitotic hyperphosphorylation of NPM1 reduces, rather than enhances, its charge blockiness and suppresses its strong LLPS propensity, leading to dissolution of the nucleoli (Fig. 5). The opposing effects of mitotic phosphorylation of Ki-67 and NPM1 on their LLPS, together with their cell cycle-specific interaction (Extended Data Fig. 8d), underlie the morphological changes of nucleoli and the chromosome periphery during mitosis (Extended Data  Fig. 8e). Our phosphoproteomic analyses demonstrated that mitotic hyperphosphorylation changes the charge blockiness of IDRs in several other nucleolar proteins (Extended Data Fig. 9), suggesting that their LLPS is also regulated by charge blockiness-enhancing or charge blockiness-reducing phosphorylation. Notably, the average charge block size converges to ~30-40 amino acids, indicating that this charge block size is the most suitable for a polypeptide to undergo regulatable LLPS in an intracellular milieu.
In summary, the blockiness-enhancing or blockiness-reducing phosphorylation described here is distinct from previously reported phosphorylation-based regulatory mechanisms and may represent a general mechanism that regulates the behaviour of a broad spectrum of phosphoproteins and assembly and disassembly of intracellular membraneless organelles and structures.

online content
Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/ s41556-022-00903-1.

Materials.
All chemical reagents used in this study were purchased from Nacalai Tesque unless otherwise indicated.

Protein sequence analysis. The mitotic phosphosites in human Ki-67 and NPM1
were reported in our previous study 16 . The human Ki-67 and NPM1 sequences were obtained from the UniProt database (accession numbers P46013 and P06748, respectively). Charge distribution was calculated as the sum of the charges (Arg and Lys, +1; Glu and Asp, −1; phospho-Ser and phospho-Thr, −2) in the indicated window range. A charge block was designated when the area of the charge plot (window size: 35 amino acids) was larger than 20. Multiple sequence alignment was performed using Clustal Omega (https://www.ebi.ac.uk/Tools/msa/clustalo/). D seg and B LC were calculated with the equation described in Supplementary Note. We chose to use B LC over other charge patterning parameters such as sequence charge decoration 43 and κ (ref. 44 ), because B LC employs a larger block size, more appropriately capturing the longer charge tracts that we believe are important in Ki-67.

DNA construction.
Complementary DNA of human Ki-67 (short isoform) was obtained as described previously 45 . Fragments of the WT Ki-67 RD, LR domain (amino acids 2,578-2,896) and N-terminal domain (amino acids 1-639 (corresponding to amino acids 1-135 and 496-999 of the long isoform)) as well as human NPM1 (amino acids 105-250) were amplified by PCR and subcloned into pET28a(+) (Novagen) for expression in Escherichia coli and/or pEGFP for mammalian expression. The nucleotide sequences of primers are presented in Supplementary Table 1. cDNA fragments encoding phosphomimetic mutants and charge-block mimetic mutants of Ki-67 and NPM1 were synthesized at Thermo Fisher Scientific. The amino-acid sequences of all mutants that were used in this study are presented in Supplementary Table 2. For bacterial expression, the codon usage was optimized for E. coli without changing the amino-acid sequence. To generate tandem repeats of Ki-67 R12 and R7, the DNA fragment encoding R12 was cleaved out from the expression vector with Xho I and Sal I digestion and ligated into the same expression construct digested with Sal I. Through these procedures, the number of R12 was increased up to 12. All of these homogeneous repeat constructs contained the linker sequence 'GHTEESVEDD' between each repeat unit.

Cell culture, synchronization and transfection. HeLa cells (ATCC, CCL-2.2)
were cultured in Dulbecco's modified Eagle's medium (DMEM, Sigma-Aldrich) supplemented with 10% foetal bovine serum (FBS, Gibco) at 37 °C in the presence of 5% CO 2 . The Ki-67 KO HCT116 cell line was described previously 46 and was cultured in high-glucose DMEM supplemented with 10% FBS and penicillinstreptomycin at 37 °C in the presence of 5% CO 2 . Cells were transfected with the plasmids using PEI-MAX (Polysciences). To induce mitotic arrest, cells were treated with 0.2 µM nocodazole for 15 h. For microscopic observation, cells on a cover glass (Matsunami Glass) were fixed with 4% paraformaldehyde at room temperature for 15 min and mounted with Vectashield (Vector Laboratories) containing Hoechst 33342.
To purify His 6 -tagged protein under a native condition, the cell pellet was dissolved in lysis buffer (50 mM Tris-HCl, 500 mM NaCl, 1 mM MgCl 2 , 2 mM 2-mercaptoethanol, 1 mM phenylmethylsulfonyl fluoride, 20 mM imidazole, lysozyme and DNase I, pH 7.4) and subjected to three rounds of quick freezethaw cycles. The cell debris was removed by centrifugation (12,000g, 20 min, 4 °C) and the supernatant was mixed with Ni-NTA beads at 4 °C for 1 h. The beads were then washed with wash buffer (50 mM Tris-HCl, 500 mM NaCl, 2 mM 2-mercaptoethanol and 20 mM imidazole, pH 7.4) three times and eluted stepwise with increasing concentrations (50, 100, 200, 300, 400 and 500 mM) of imidazole in wash buffer. The eluted protein was dialysed against low-salt buffer (50 mM Tris-HCl, 50 mM NaCl and 2 mM 2-mercaptoethanol, pH 7.4) at 4 °C for 3 h and then subjected to ion-exchange chromatography (Hi-Trap Q, GE Healthcare). The eluted fraction was collected, dialysed against assay buffer (50 mM HEPES and 100 mM NaCl, pH 7.4) at 4 °C, concentrated using Amicon centrifugal filters (Millipore) and stored at −80 °C in small aliquots. The amount of RNA contamination in the individual protein preparations was quantified using a fluorescent probe for RNA (QuantiFluor RNA, Promega) and was 0.1-0.7% (w/w).
In vitro LLPS assay. Lyophilized protein was dissolved into dissolving buffer (2 M guanidine hydrochloride, 100 mM Tris-HCl pH 8.0 and 10 mM HEPES) to a final concentration of 4 mM. For fluorescence microscopic observation, protein was incubated with 10 µM ATTO488-maleimide (ATTO-TEC) at room temperature for 1 h and then with 5 mM dithiothreitol at room temperature for 1 h or at 4 °C overnight. The labelled protein solution was diluted in droplet buffer (50 mM HEPES, 100 mM NaCl and 15% (w/v) PEG3350 (Sigma-Aldrich), pH 7.4) at a 1:100 ratio, incubated at room temperature for 30 min and transferred to a 96-well clear-bottom plate (Greiner Bio-One) for microscopic observation (FV3000, Olympus). The final concentration of protein was 40 μM unless otherwise indicated. For protein with multiple repeats, the final protein concentration is indicated in the figure legend. For the turbidity assay, protein in dissolving buffer was sequentially diluted with the same buffer, and then mixed with droplet buffer at 1:50. The mixture was incubated at room temperature for 10 min and transferred to a microcuvette. The optical density at 600 nm (OD 600 ) was measured using a V-630 spectrophotometer (JASCO). The C sat value was defined by the concentration at which the turbidity was at half-maximal value 10

Microscopic observation, image processing and image analysis.
For the observation of fluorescence signals, a confocal laser-scanning microscope system (FV3000, Olympus) was used. For live-cell imaging, a stage chamber (Tokai Hit) was used to maintain the temperature and moisture and CO 2 levels. Phenol red-free DMEM supplemented with 10% FBS and 1 µg ml −1 Hoechst 33342 was used to visualize chromosomes if necessary. The images obtained were processed and analysed using MetaMorph (Molecular Devices), Fiji 47 or Python 2 or 3 with add-on libraries (Numpy, Scipy, Pandas, Matplotlib, OpenCV and seaborn).

Statistics and reproducibility.
Methods of statistical analysis and sample size are indicated in the figure legends.
No statistical methods were used to predetermine sample size. Sample sizes were estimated empirically on the basis of pilot experiments and previously performed experiments with similar setup to provide sufficient sample sizes for statistical analysis. No data were excluded from the analyses with the exception of the image analysis of droplet. For the quantification of droplet, ones with higher eccentricity than criterion (0.7) were excluded. For droplet assay, sample and measurement order was randomized. The area of microscopic observation was randomly determined. The investigators were not blinded to allocation during experiments and outcome assessment. Turbidity assay was performed three times, and microscopic observation, gel electrophoresis, western blotting and electrophoretic mobility shift assay were performed at least twice.
Reporting Summary. Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Data availability
Amino-acid sequences of human Ki-67 and human NPM1 can be obtained from UniProt database (accession number P46013 for Ki-67 and P06748 for NPM1). Source data are provided with this paper. All other data supporting the findings of this study are available from the corresponding author on reasonable request.  Fig. 2b. b, LLPS assay of R7. amino-acid sequences of human Ki-67 R7 (wild-type (WT) and phosphomimetic mutant of mitotic phosphosites (Pm)). The mitotic phosphosite is denoted with an asterisk (*). Positive and negative charge blocks (see Methods) are highlighted in cyan and red, respectively. Charge plots (window size: 25 amino acids) with B LC values (left panels) are shown. Fluorescence images of an in vitro droplet assay and the statistical analysis of the fluorescence intensity are presented (middle and right panels). Bar, 30 µm. c, Turbidity assay of R7_WT and R7_Pm. One representative result is shown (out of three). The C sat values are presented as mean ± standard deviation from three independent experiments. d, Circular dichroism (CD) spectrum of purified R12 fragments. Purified R12 (WT and Pm9) were subjected to CD spectrum measurement in 50 mM HEPES, 100 mM NaCl (pH. 7.4) at 25 °C. Source numerical data are available in Source Data. Fig. 4 | llPS is governed by charge blockiness rather than net charge. a, Relationship between C sat and D seg . The C sat values of the mutants and WT of R12 were obtained by the turbidity assay described in Fig. 2c and plotted against D seg . Error bars reflect standard deviation of the mean (n = 3 independent measurements). b, amino-acid sequences of CBm-5-16 and charge plots (window size: 25 amino acids). The B LC values are presented. Positive and negative charge blocks (see Methods) are highlighted in the amino-acid sequence with cyan and red, respectively. The mitotic phosphosite is denoted with an asterisk (*). c, Relationship between C sat and D seg in the mutants shown in b (CBm-5 -CBm-16). The C sat values were obtained by the turbidity assay described in Fig. 2d and plotted against D seg . Error bars reflect standard deviation of the mean (n = 3 independent measurements). d, Relationship between C sat and the net charge of the R12 (WT, Pm9, CBm1-16) and R7 (WT and Pm). The C sat values obtained by the turbidity assay described in Fig. 2c,d were plotted against the net charge. Error bars reflect standard deviation of the mean (n = 3 independent measurements). Source numerical data are available in Source Data. reversibly associates and dissociates from mitotic chromosomes upon ammonium acetate treatment. Ki-67-KO cells expressing EGFP-Ki-67 were treated with 100 mM ammonium acetate for 10 min and then returned to normal culture medium after washing with PBS. Time-lapse fluorescence images are shown in (a). Bar, 5 µm. The total EGFP signal intensity at the chromosomes was quantified and plotted along the time course (each line shows the data from an individual cell (n = 4)) (b). c, Ki-67 shows liquid-like behaviour on the mitotic chromosome periphery. FRaP analysis of EGFP-(WT) 8 -LR expressed in HeLa cells. Time-lapse fluorescence images before and after bleaching are shown. The region surrounded by a circle was bleached using 488-nm laser light and the fluorescence intensity in the area was measured and plotted (mean ± SD, n = 38) (right panel). The fitting result from 38 cells is shown. Signal intensity was quantified using MetaMorph (Molecular Devices). Curve-fitting was performed using Python2 or 3 with accompanying libraries (Numpy, Scipy, Pandas, Matplotlib), using the equation described in Supplementary Note. Bar, 2 µm. d, Fluorescence images of mitotic HeLa cells expressing LR-free RDs. EGFP-fused WT R12 ((WT) 4 , (WT) 8 ) and phosphomimetic mutants ((Pm9) 4 , (Pm9) 8 ), were expressed in HeLa cells. Cells were fixed, stained with Hoechst33342, and observed by confocal fluorescence microscopy. Bar, 5 μm. e, Localization of R12 repeat (EGFP-(WT) 4 -LR, EGFP-(WT) 8 -LR, EGFP-(a9) 4 -LR) and EGFP-(a9) 8 -LR) in mitotic HeLa cells. DNa was stained with Hoechst33342. Magnified images (square (3.5×3.5 µm)) are shown in the insets. Bar, 5 µm. Source numerical data are available in Source Data.